Question

in a cylindrical vessel of radius 10 cm containing some water 9000 small spherical ball are dropped which are completely immersed in water which raises the water level if each spherical ball is of radius 0.5 cm then find the rise in the level of water in the vessel​

Answer 1

Answer:

please see the attached picture for solution.

Answer 2

Given:

cylindrical vessel radius =10 cm

containing 9000 small spherical balls so each ball radius =0.5 cm

To find:

level of water in the vessel​=?

Solution:

Formula:

The volume of a cylinder (V)= $\pi r^2 h$

The volume of a sphere =$\frac{4}{3}\pi r^3$

$\bold{\textttt{\ raises \ volume \ = \ volume \ of \ a \ sphere \times \ 9000} }$

Solve:

$\to \pi r^2h=\frac{4}{3}\pi r^3\times 9000\\\\\to (10)^2\times h=\frac{4}{3} \times (0.5)^3\times 9000\\\\\to 100\times h=\frac{4}{3}\times (0.125)\times 9000\\\\\to 100\times h=4\times 0.125\times 3000\\\\\to h=\frac{4\times 0.125\times 3000}{1000}\\\\\to h=\frac{4\times 125\times 3000}{100\times 1000}\\\\\to h=\frac{4\times 125\times 3}{100}\\\\\to h=\frac{4\times 5\times 3}{4}\\\\\to h= 3\times 5\\\\\to h = 15 \ cm$

The final answer is "15 cm".